Here are the steps to answer this question:
1. Find the denominator. Since there is 8 possible outcomes, our denominator will be 8.
2. Find the numerator. To do this we need to find out of all the 8 possible outcomes, how many are them are y. Since its only 1 y, the numerator will be 1.
3. Now all we have to do now is make our fraction. The 8 possible outcomes given, only one of them has y which means that our fraction will be 1/8.
4. Answer: 1/8 or .125 or 12.5% chance for the spinner to land on y. I hope this helps!
For this case we have that a quadratic equation is of the form:
![ax ^ 2 + bx + c = 0](https://tex.z-dn.net/?f=ax%20%5E%202%20%2B%20bx%20%2B%20c%20%3D%200)
The roots are given by:
![x = \frac {-b \pm \sqrt {b ^ 2-4 (a) (c)}} {2 (a)}](https://tex.z-dn.net/?f=x%20%3D%20%5Cfrac%20%7B-b%20%5Cpm%20%5Csqrt%20%7Bb%20%5E%202-4%20%28a%29%20%28c%29%7D%7D%20%7B2%20%28a%29%7D)
We have the following equation:
![4x ^ 2-3x + 9 = 2x + 1\\4x ^ 2-3x-2x + 9-1 = 0\\4x ^ 2-5x + 8 = 0](https://tex.z-dn.net/?f=4x%20%5E%202-3x%20%2B%209%20%3D%202x%20%2B%201%5C%5C4x%20%5E%202-3x-2x%20%2B%209-1%20%3D%200%5C%5C4x%20%5E%202-5x%20%2B%208%20%3D%200)
We look for the roots:
![x = \frac {- (- 5) \pm \sqrt {(- 5) ^ 2-4 (4) (8)}} {2 (4)}\\x = \frac {5 \pm \sqrt {25-128}} {8}\\x = \frac {5 \pm \sqrt {-103}} {8}](https://tex.z-dn.net/?f=x%20%3D%20%5Cfrac%20%7B-%20%28-%205%29%20%5Cpm%20%5Csqrt%20%7B%28-%205%29%20%5E%202-4%20%284%29%20%288%29%7D%7D%20%7B2%20%284%29%7D%5C%5Cx%20%3D%20%5Cfrac%20%7B5%20%5Cpm%20%5Csqrt%20%7B25-128%7D%7D%20%7B8%7D%5C%5Cx%20%3D%20%5Cfrac%20%7B5%20%5Cpm%20%5Csqrt%20%7B-103%7D%7D%20%7B8%7D)
We have to:
![i ^ 2 = -1](https://tex.z-dn.net/?f=i%20%5E%202%20%3D%20-1)
So:
![x = \frac {5 \pm \sqrt {103i ^ 2}} {8}\\x = \frac {5 \pm i \sqrt {103}} {8}](https://tex.z-dn.net/?f=x%20%3D%20%5Cfrac%20%7B5%20%5Cpm%20%5Csqrt%20%7B103i%20%5E%202%7D%7D%20%7B8%7D%5C%5Cx%20%3D%20%5Cfrac%20%7B5%20%5Cpm%20i%20%5Csqrt%20%7B103%7D%7D%20%7B8%7D)
We have two imaginary roots:
![x_ {1} = \frac {5 \ + i \sqrt {103}} {8}\\x_ {2} = \frac {5 \ -i \sqrt {103}} {8}](https://tex.z-dn.net/?f=x_%20%7B1%7D%20%3D%20%5Cfrac%20%7B5%20%5C%20%2B%20i%20%5Csqrt%20%7B103%7D%7D%20%7B8%7D%5C%5Cx_%20%7B2%7D%20%3D%20%5Cfrac%20%7B5%20%5C%20-i%20%5Csqrt%20%7B103%7D%7D%20%7B8%7D)
Answer:
![x_ {1} = \frac {5 \ + i \sqrt {103}} {8}\\x_ {2} = \frac {5 \ -i \sqrt {103}} {8}](https://tex.z-dn.net/?f=x_%20%7B1%7D%20%3D%20%5Cfrac%20%7B5%20%5C%20%2B%20i%20%5Csqrt%20%7B103%7D%7D%20%7B8%7D%5C%5Cx_%20%7B2%7D%20%3D%20%5Cfrac%20%7B5%20%5C%20-i%20%5Csqrt%20%7B103%7D%7D%20%7B8%7D)
Let
x-------------> pounds of granola-----------> <span>$3 per pound
</span>y-------------> pounds of raisins-----------> $2 per pound
z------------ > price per <span>pounds of the trail mix
</span>
we have that
z=3x+2y--------------------- > this is the equation
for x=3 pounds of granola and y=<span>0.75 pounds of raisins
z=3*3+2*0.75=</span>$10.5 of <span>trail mix</span>
Correct me if I'm wrong but I think since her car goes 35 miles per gallon & has 100 gallons then she would be able to travel for 3500 miles.So,she would be able to drive to her cousins house.